The Sequential Construction of Minimal Partial Realizations from Finite Input–Output Data

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Abstract
Any strictly proper transfer function matrix of a continuous or discrete, linear, constant, multivariable system can be written as the product of a numerator polynomial matrix with the inverse of another polynomial matrix, the denominator. Since a realization is easily constructed from the polynomial matrix representation, the minimal partial realization problem is translated to that of extracting -a minimal order partial denominator polynomial matrix from a finite length matrix sequence. It is shown that minimal partial denominator matrices evolve recursively that is, a minimal partial denominator matrix for any finite length sequence is a combination of the minimal partial denominator matrices of its proper subsequences. A computationally efficient algorithm that sequentially constructs a minimal partial denominator matrix for a given finite length sequence is presented. A theorem by Anderson and Brasch leads to a definition of uniqueness for the resulting denominator matrix based upon its invariant fac...
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